Unperturbed Beam Research Articles

Bifurcation analysis of electron-acoustic waves in electron beam-plasma with suprathermal electrons

It has investigated the properties of nonlinear electron-acoustic waves propagating in a four-component collisionless, unmagnetized plasma. The system consists of cool inertial background electrons of temperature T c , the cool inertial electron beam of temperature T b , hot inertialess suprathermal electrons modeled by a κ-distribution of temperature T h , and ions. The nonlinear modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation that characterizes the electron acoustic waves in such a plasma model is derived. The wave solutions of the resultant mKdV-Burgers equation are investigated using planar dynamical system bifurcation theory. The unperturbed hot, cool, and beam electron densities and the superthermal electron parameter are revealed to have a considerable influence on the nonlinear electron-acoustic traveling waves and the associated electric fields. The system evolves also monotonic shock waves when the dissipation term dominates over the dispersion term. The current model might be useful for understanding the generation of nonlinear electron-acoustic waves in a variety of astrophysical plasma settings, including the Earth's magnetosphere.

Spatiotemporal Electron Beam Focusing through Parallel Interactions with Shaped Optical Fields.

The ability to modulate free electrons with light has emerged as a powerful tool to produce attosecond electron wave packets. However, research has so far aimed at the manipulation of the longitudinal wave function component, while the transverse degrees of freedom have primarily been utilized for spatial rather than temporal shaping. Here, we show that the coherent superposition of parallel light-electron interactions in transversally separate zones allows for a simultaneous spatial and temporal compression of a convergent electron wave function, enabling the formation of sub-Ångström focal spots of attosecond duration. Specifically, spots spanning just ∼3% of the light optical cycle are shown to be formed, accompanied by an increase by only a factor of 2 in spatial extension relative to an unperturbed beam. The proposed approach will facilitate the exploration of previously inaccessible ultrafast atomic-scale phenomena, in particular enabling attosecond scanning transmission electron microscopy.

Evidence of oblique electron acoustic solitary waves triggered by magnetic reconnection in Earth’s magnetosphere

Motivated by the recent Magnetospheric Multiscale (MMS) observations of oblique electron acoustic waves, we addressed the generation mechanism of the observed waves by utilizing the reductive perturbation technique. A nonlinear Zakharov-Kuznetsov (ZK) equation is derived for a collisionless, magnetised plasma composed of cool inertial background electrons, cool inertial electron beam, hot inertialess suprathermal electrons; represented by a κ-distribution, and stationary ions. Moreover, the instability growth rate is derived by using the small-k perturbation expansion method. Our findings revealed that the structure of the electrostatic wave profile is significantly influenced by the external magnetic field, the unperturbed hot, cool, and electron beam densities, the obliquity angle, and the rate of superthermality. Such parameters also have an effect on the instability growth rate. This study clarifies the characteristics of the oblique electron solitary waves that may be responsible for changing the electron and ion distribution functions, which alter the magnetic reconnection process. Moreover, the increase of the growth rate with the plasma parameters could be a source of anomalous resistivity that enhances the rate of magnetic reconnection.

Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge

Transformations of the vortex beams structure subjected to sectorial perturbation were theoretically and experimentally studied. The analysis was based on computing (measuring) the vortex spectrum that enables us to find the orbital angular momentum (OAM) and Shannon entropy (informational entropy). We have revealed that, in the general case, the number of vortices caused by an external perturbation is not related to the topological charge. For arbitrary perturbation, the topological charge remains equal to the initial topological charge of the unperturbed vortex beam. Growth of the vortex number induced by perturbations is associated with the optical uncertainty principle between the sectorial angle and the OAM. The computer simulation has shown that OAM does not depend on the number of vortices induced by perturbations. Moreover, two maxima are formed both in the positive and negative regions of the vortex spectrum. As a result, the OAM does not practically change in a wide range of perturbation angles from 0 to 90 °. However, at large perturbation angles, when the energy is almost equally redistributed between the vortex modes with opposite signs of the topological charge, the OAM rapidly decreases. At the same time, the Shannon entropy monotonically increases with growing perturbation angle. This is due to the fact that the entropy depends only on the number of vortex states caused by external perturbations.

Far-Field Spatial Structure of a Diffracted Airy Beam with Stopping of Its Lateral Maxima

The formation of the spatial spectrum of Airy beams under conditions of partial stopping of their aperture is studied theoretically and experimentally. It is shown that the structure of the field in the far field of exponential Airy beams depends on the relationship between the characteristic self-reconstruction length of the beams and the near boundary of the far field. If the boundary of the far field exceeds the reconstruction length, then the spatial structure of the field evolves through a stage of partial recovery of the initial beam, after which a far field is formed that differs substantially from that for an unperturbed beam. The distinctive feature of the field in the far field is a multipeak spatial structure with an envelope that is close to gaussian. Then the number of peaks equals the number of the stopped side maximum of the original Airy beam.

Absolute absorption cross sections from photon recoil in a matter-wave interferometer.

We measure the absolute absorption cross section of molecules using a matter-wave interferometer. A nanostructured density distribution is imprinted onto a dilute molecular beam through quantum interference. As the beam crosses the light field of a probe laser some molecules will absorb a single photon. These absorption events impart a momentum recoil which shifts the position of the molecule relative to the unperturbed beam. Averaging over the shifted and unshifted components within the beam leads to a reduction of the fringe visibility, enabling the absolute absorption cross section to be extracted with high accuracy. This technique is independent of the molecular density, it is minimally invasive and successfully eliminates many problems related to photon cycling, state mixing, photobleaching, photoinduced heating, fragmentation, and ionization. It can therefore be extended to a wide variety of neutral molecules, clusters, and nanoparticles.

Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory

Vector diffraction theory is applied to the case of focused TEM(00) Gaussian beams passing through a spatially limiting aperture in order to investigate the propagation of these clipped focused-Gaussian beams. Beam distributions at different axial distances show that a traditional M(2) propagation model cannot be used for the propagation of clipped focus-Gaussian beams. Using Luneberg's vector diffraction theory and Fresnel approximations, an analytical model for the on-axis transverse and longitudinal electric fields and intensity distributions is presented including predictions of the maximum obtainable intensity. In addition, an analytical expression is provided for the longitudinal component of the electric field of a TEM(00) mode unperturbed Gaussian beam. Experimental results are also presented and compared to the model's predictions.

Assessment of the setup dependence of detector response functions for mega‐voltage linear accelerators

Accurate modeling of beam profiles is important for precise treatment planning dosimetry. Calculated beam profiles need to precisely replicate profiles measured during machine commissioning. Finite detector size introduces perturbations into the measured profiles, which, in turn, impact the resulting modeled profiles. The authors investigate a method for extracting the unperturbed beam profiles from those measured during linear accelerator commissioning. In-plane and cross-plane data were collected for an Elekta Synergy linac at 6 MV using ionization chambers of volume 0.01, 0.04, 0.13, and 0.65 cm3 and a diode of surface area 0.64 mm2. The detectors were orientated with the stem perpendicular to the beam and pointing away from the gantry. Profiles were measured for a 10 x 10 cm2 field at depths ranging from 0.8 to 25.0 cm and SSDs from 90 to 110 cm. Shaping parameters of a Gaussian response function were obtained relative to the Edge detector. The Gaussian function was deconvolved from the measured ionization chamber data. The Edge detector profile was taken as an approximation to the true profile, to which deconvolved data were compared. Data were also collected with CC13 and Edge detectors for additional fields and energies on an Elekta Synergy, Varian Trilogy, and Siemens Oncor linear accelerator and response functions obtained. Response functions were compared as a function of depth, SSD, and detector scan direction. Variations in the shaping parameter were introduced and the effect on the resulting deconvolution profiles assessed. Up to 10% setup dependence in the Gaussian shaping parameter occurred, for each detector for a particular plane. This translated to less than a +/- 0.7 mm variation in the 80%-20% penumbral width. For large volume ionization chambers such as the FC65 Farmer type, where the cavity length to diameter ratio is far from 1, the scan direction produced up to a 40% difference in the shaping parameter between in-plane and cross-plane measurements. This is primarily due to the directional difference in penumbral width measured by the FC65 chamber, which can more than double in profiles obtained with the detector stem parallel compared to perpendicular to the scan direction. For the more symmetric CC13 chamber the variation was only 3% between in-plane and cross-plane measurements. The authors have shown that the detector response varies with detector type, depth, SSD, and detector scan direction. In-plane vs. cross-plane scanning can require calculation of a direction dependent response function. The effect of a 10% overall variation in the response function, for an ionization chamber, translates to a small deviation in the penumbra from that of the Edge detector measured profile when deconvolved. Due to the uncertainties introduced by deconvolution the Edge detector would be preferable in obtaining an approximation of the true profile, particularly for field sizes where the energy dependence of the diode can be neglected. However, an averaged response function could be utilized to provide a good approximation of the true profile for large ionization chambers and for larger fields for which diode detectors are not recommended.

Apparatus to study crystal channeling and volume reflection phenomena at the SPS H8 beamline

A high performance apparatus has been designed and built by the H8-RD22 collaboration for the study of channeling and volume reflection phenomena in the interaction of 400 GeV/c protons with bent silicon crystals, during the 2006 data taking in the external beamline H8 of the CERN SPS. High-quality silicon short crystals were bent by either anticlastic or quasimosaic effects. Alignment with the highly parallel (8 murad divergence) proton beam was guaranteed through a submicroradian goniometric system equipped with both rotational and translational stages. Particle tracking was possible by a series of silicon microstrip detectors with high-resolution and a parallel plate gas chamber, triggered by various scintillating detectors located along the beamline. Experimental observation of volume reflection with 400 GeV/c protons proved true with a deflection angle of (10.4+/-0.5) murad with respect to the unperturbed beam, with a silicon crystal whose (111) planes were parallel to the beam.

SU-FF-T-141: Determination of a Chamber Independent Profile

Purpose: Calculation of the inherent beam profile and its accuracy are highly important in the dosimetric precision of treatment planning. However, perturbations are incorporated into the profile due to finite detector size and non-water equivalency. We investigate a potential method for extracting the unperturbed beam profile from that of the measured profile using ion chambers for the purpose of performing de-convolution of the detector response functions. Method and Materials: Beam profiles were obtained using a 0.04 cm3 ion chamber orientated orthogonally to the beam direction. Scans were made at 10 cm depth and the SSD varied between 86 and 120 cm. The Data were extrapolated to a distance such that perturbation effects would be negligible, and then geometrically scaled to 90 SSD. The resulting profile was compared to penumbra measurements using diodes. Results: A linear relationship was observed between off axis dose location and increasing SSD i.e. the location of the 50% increased linearly along the off axis profile with changing SSD. The extrapolated and scaled profile demonstrated improved penumbra 0.74 cm to 0.5 cm for the 80–20 % region compared to the raw profile and was comparable with that obtained from diode measurements. Conclusion: We have demonstrated a potential method for obtaining the unperturbed beam profile from a megavoltage LINAC. The linearity of profile data with SSD has been exploited to remove chamber effects such as volume averaging that commonly degrade the penumbra in order to obtain the inherent beam profile. This work supported in part by SBIR Contract No HHSN261200522014C, ABD Contract No. N43-CM-52214 and Sun Nuclear Corporation.

Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation

This study deals with the nonlinear dynamics associated with large deformation of abeam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic-Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deflection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic-Frisch-Fay exact solution is given in terms of elliptic functions. A curve fit of the exact solution up to eleventhorder is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases

Nonlinear Dynamics of a Sliding Beam on Two Supports and its Efficacy as a Non-Traditional Isolator

This study deals with the nonlinear dynamics associated with large deformations of a beam sliding on two knife-edge supports under external excitation. The beam will be referred to as Gospodnetic-Frisch-Fay beam, after the researchers who reported its static deformation in a closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deflection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll restoring moment of ships. The Gospodnetic-Frisch-Fay exact solution is given in terms of elliptic functions, and a curve fit of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the initial conditions. The steady state response and transmissibility of the beam are predicted using multiple-scales method and numerical simulation. The transmissibility of the nonlinear beam outperforms linear isolators only at the linear resonance frequency. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitudes and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases. Under random excitation, the response probability density function is obtained in a closed form and the response mean energy is found to depend nonlinearly on the excitation spectral density.

Generation of intense secondary pulsed molecular beams of high kinetic energy controllable by a powerful IR laser

A method for generation of intense secondary pulsed molecular beams and beams of radicals of high kinetic energy controllable by a powerful IR laser is described. A pressure shock (shock wave) is used as a source of secondary beams. The pressure shock is formed in interaction between an intense pulsed supersonic molecular beam (or flow) and a solid surface. The characteristics of the secondary beams were studied. Their intensities and the degree of gas cooling in them were shown to be comparable with the corresponding characteristics of the unperturbed primary beam. The acceleration of molecules in the secondary beam is achieved due to vibrational excitation of them by high-power IR laser pulse in the pressure shock and subsequent vibrational to translational (V–T) relaxation, which occurs when a gas expands through the orifice into a vacuum. Intense [⩾1020 molecules/(sr s)] beams of SF6 and CF3I molecules with kinetic energies approximately equal to 1.5 and 1.2 eV, respectively, were generated in the absence of carrier gases. The SF6 molecular beams with kinetic energies approximately from 2.5 to 2.7 eV with carrier gases H2, He and CH4 (SF6/carriergas=1/10) were obtained. The possibility of generation of intense beams of cold radicals by this method is demonstrated. The intense beams of cold and accelerated CF3 radicals were generated when the CF3I molecules in the shock were dissociated by high-power CO2 laser radiation. The spectral and energetic characteristics of acceleration of SF6 and CF3I molecules in the secondary beams were studied. The optimal conditions were found for obtaining high-energy molecules.

The formation of an intense secondary pulsed molecular beam and obtaining accelerated molecules and radicals in it

A method for obtaining an intense secondary pulsed molecular beam is described. The kinetic energy of molecules in the beam can be controlled by vibrational excitation of the molecules in the source under high-power IR laser radiation. A compression shock (shock wave) is used as a source of secondary beams. The shock wave is formed in interaction between an intense pulsed supersonic molecular beam (or flow) and a solid surface. The characteristics of the secondary beam were studied. Its intensity and the degree of gas cooling in it were comparable with the corresponding characteristics of the unperturbed primary beam. Vibrational excitation of molecules in the shock wave and subsequent vibrational-translational relaxation, which occurs when a gas is expanded in a vacuum, allow the kinetic energy of molecules in the secondary beam to be substantially increased. Intense [≥1020 molecules/(sr s)] beams of SF6 and CF3I molecules with kinetic energies approximately equal to 1.5 and 1.2 eV, respectively, were generated in the absence of carrier gases, and SF6 molecular beams with kinetic energies approximately equal to 2.5 and 2.7 eV with He (SF6/He=1/10) and H2 (SF6/H2=1/10) as carrier gases, respectively, were obtained. The spectral and energy characteristics of acceleration of SF6 molecules in the secondary beams were studied. The optimal conditions were found for obtaining high-energy molecules. The possibility of accelerating radicals in secondary molecular beams was demonstrated.

Effects of Cooling on the Propagation of Magnetized Jets

We present multidimensional simulations of magnetized radiative jets appropriate to young stellar objects (YSOs). Magnetized jets subject to collisionally excited radiative losses have not, as yet, received extensive scrutiny. The purpose of this Letter is to articulate the propagation dynamics of radiative MHD jets in the context of the extensive jet literature. Most importantly, we look for morphological and kinematic diagnostics that may distinguish hydrodynamic protostellar jets from their magnetically dominated cousins. Our simulations are axisymmetric (2.5 dimensions). A toroidal (B) field geometry is used. Our models have high sonic Mach numbers (M -->s ? 10) but lower fast-mode Mach number (M -->f ? 5). This is approximately the case for jets formed via disk-wind or X-wind models?currently the consensus choice for launching and collimating YSO jets. Time-dependent radiative losses are included via a coronal cooling curve. Our results demonstrate that the morphology and propagation characteristics of strongly magnetized radiative jets can differ significantly from jets with weak fields. In particular, the formation of nose cones via postshock hoop stresses leads to narrow bow shocks and enhanced bow shock speeds. In addition, the hoop stresses produce strong shocks in the jet beam, which contrasts with the relatively unperturbed beam in radiative hydrodynamic jets. Our simulations show that pinch modes produced by magnetic tension can strongly affect magnetized protostellar jets. These differences may be useful in observational studies designed to distinguish between competing jet collimation scenarios.

Sideband optical–optical double resonance Zeeman spectroscopy. I. Theory of saturation and line shape behavior

Several variants of the one-laser, two-color technique of sideband optical–optical double resonance Zeeman (SOODRZ) spectroscopy, which enables Zeeman and hyperfine splittings to be measured at sub-Doppler resolution, are described; a detailed theory of the line shape and signal-to-noise ratio for each variant is also presented. In the single-frequency variant of SOODRZ spectroscopy, radio frequency sidebands are imposed onto a single-frequency continuous wave laser beam to determine energy splittings between pairs of closely spaced levels. Each pair of closely spaced levels is coupled to a third isolated level by optical transitions and is tuned into resonance by the Zeeman effect. A theoretical treatment of the SOODRZ effect is presented here. It is shown that both the real and imaginary contributions to the complex third-order optical susceptibility tensor χ(3) can be observed and that the SOODRZ signal originates from a cross term between the amplitude of the unperturbed frequency-modulated beam of the laser and the nonlinear signal amplitude Re{EL*⋅ENL}. The SOODRZ signal is directly proportional to ΔNμ4MI20 (where M is the modulation index), rather than (ΔN)2, μ8, and I30 as in degenerate four-wave mixing and other nonlinear spectroscopies, which means the detection sensitivity of SOODRZ spectroscopy is considerably higher for low laser intensities and at lower number densities. Moreover, the linewidth of the sub-Doppler feature is independent of the both the Doppler width of the optical transition and the natural width of the common linked level and, hence, is immune from the effects such as upper state predissociation. Two different types of modulators, acousto-optic and electro-optic, can be used in the single-frequency variant of SOODRZ spectroscopy. The unique features of SOODRZ schemes incorporating both types of modulators are described. SOODRZ spectroscopy can also be performed with a multimode broadband laser, where the adjacent cavity modes serve the same function as the sidebands in the single-frequency version. Examples of such multimode SOODRZ spectra will be presented as well. The effect of different detection schemes (i.e., nearly crossed polarizers and/or coherent detection), laser frequency detuning relative to the center of the absorption line, and ac magnetic field modulation conditions on the intensity, phase, and functional form of the sub-Doppler double resonance line shape will be discussed here. The simplest possible form of the SOODRZ line shape is a second derivative of a Lorentzian.

Fourier optics approach to far forward scattering and related refractive index phenomena in laboratory plasmas

The transmission of a gaussian beam of electromagnetic radiation through a refracting medium such as plasma containing within it a localized sinusoidal disturbance, is described entirely in terms of refraction and diffraction. The lowest order terms of an expansion for the intensity profile of a beam in the front focal plane of a lens situated a focal length beyond a beam waist in the medium are identified with well-known optical effects usually treated independently, including shadowgraph, scattering, and schlieren. The latter is shown to be indistinguishable from spontaneous heterodyning of the scattered radiation with the unperturbed beam, and is sensitive to frequency, wavelength, and the location of the disturbance in the medium. An experiment using a HeNe laser with monochromatic ultrasound in atmospheric air has verified the predictions of the model over a wide range of conditions. As a plasma diagnostic, the method may offer a unique means of measuring otherwise inaccessible very long wavelength instabilities such as trapped ion modes in large Tokamaks like JET.

Theory of the free-electron laser in combined helical pump and axial guide fields

The linearized theory of a free-electron-laser amplifier consisting of a relativistic electron beam transported along the axis of a helical wiggler in the presence of an axial guide field is solved exactly. With suitable re-identification of parameters, the theory also applies to the case where the wiggler is replaced by a circularly polarized subluminous radio-frequency pump. The dispersion relation is derived and numerical examples of solutions are presented. These indicate (a) that the use of an axial field permits operation of a laser of given high frequency and undulatory transverse velocity of the unperturbed electron beam at lower values of the pump field, (b) that the gain can be enhanced by approaching the condition of resonance between the effective frequency of the pump and the cyclotron frequency, and (c) that the breadth in frequency of the region corresponding to spatially exponentially growing operation can be much extended.

The measurement of velocity by applying schlieren-interferometry to Doppler-shifted laser light

A method is developed in which light from a laser, after being reflected, refracted, or diffracted in one selected direction by any moving solid or phase object (including particles, flames or pressure waves) is isolated by a ‘schlieren aperture’ and then allowed to interfere with an unperturbed beam. The Doppler shift in wavelength manifests itself as a beat frequency which is related theoretically to the passage of interference fringes past a small photodetector. The theoretical analysis examines various practical limitations and suggests experimental refinements. The method has been applied to moving grids, ultrasonics, flames and particles at velocities ranging from a few centimetres per second to the speed of sound.

Longitudinal Resistive Instabilities of Intense Coasting Beams in Particle Accelerators

The effect of finite resistance in the vacuum-tank walls on the longitudinal stability of an intense beam of particles in an accelerator is investigated theoretically. We show that even if the particle frequency is an increasing function of particle energy, the wall resistance can render the beam unstable against longitudinal bunching. In the absence of frequency spread in the unperturbed beam, the instability occurs with a growth rate that is proportional to (N/σ)½, where N is the number of particles in the beam and σ is the conductivity of the surface material. By means of the Vlasov equation a criterion for beam stability is obtained. In the limit of highly conducting walls the criterion involves the frequency spread in the unperturbed beam, the number of particles N, the beam energy, geometrical properties of the accelerator, but not the conductivity σ. A numerical example presented indicates that certain observations of beam behavior in the MURA 40 MeV electron accelerator may be related to the phenomenon we investigated.